Dendrites with a Countable Set of End Points and Universality

W. J. Charatonik; Evan Wright; Sophia Zafiridou

Dendrites with a Countable Set of End Points and Universality

W. J. Charatonik
, Evan Wright
, Sophia Zafiridou

Missouri University of Science and Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce a notion of ramification degree for dendrites and we use it to show that in the family of all dendrites with a countable set of end points, there is no universal element. Moreover, we characterize a dendrite with a countable set of end points using this ramification degree. Finally, we investigate the problem of existence of minimal dendrite in some families of dendrites with a countable set of end points.

Original language	American English
Journal	Houston Journal of Mathematics
State	Published - Jan 1 2013

Keywords

Dendrite
minimal space
ramification degree
scattered set
universal space

Disciplines

Mathematics
Statistics and Probability

Cite this

@article{a393fd1b32464ee08618c95a63117c31,

title = "Dendrites with a Countable Set of End Points and Universality",

abstract = " We introduce a notion of ramification degree for dendrites and we use it to show that in the family of all dendrites with a countable set of end points, there is no universal element. Moreover, we characterize a dendrite with a countable set of end points using this ramification degree. Finally, we investigate the problem of existence of minimal dendrite in some families of dendrites with a countable set of end points.",

keywords = "Dendrite, minimal space, ramification degree, scattered set, universal space",

author = "Charatonik, \{W. J.\} and Evan Wright and Sophia Zafiridou",

year = "2013",

month = jan,

day = "1",

language = "American English",

journal = "Houston Journal of Mathematics",

}

TY - JOUR

T1 - Dendrites with a Countable Set of End Points and Universality

AU - Charatonik, W. J.

AU - Wright, Evan

AU - Zafiridou, Sophia

PY - 2013/1/1

Y1 - 2013/1/1

N2 - We introduce a notion of ramification degree for dendrites and we use it to show that in the family of all dendrites with a countable set of end points, there is no universal element. Moreover, we characterize a dendrite with a countable set of end points using this ramification degree. Finally, we investigate the problem of existence of minimal dendrite in some families of dendrites with a countable set of end points.

AB - We introduce a notion of ramification degree for dendrites and we use it to show that in the family of all dendrites with a countable set of end points, there is no universal element. Moreover, we characterize a dendrite with a countable set of end points using this ramification degree. Finally, we investigate the problem of existence of minimal dendrite in some families of dendrites with a countable set of end points.

KW - Dendrite

KW - minimal space

KW - ramification degree

KW - scattered set

KW - universal space

UR - https://scholarsmine.mst.edu/math_stat_facwork/202

M3 - Article

JO - Houston Journal of Mathematics

JF - Houston Journal of Mathematics

ER -

Dendrites with a Countable Set of End Points and Universality

Abstract

Keywords

Disciplines

Other files and links

Fingerprint

Cite this